2. Computational details:
All electronic structure calculations have been carried out using the
Gaussian 09[47 ] suite of the quantum
chemistry program. For electronic structure calculations, M06-2X[48 ] functional in conjunction with
6–31G(d) basis set has been employed. M06-2X functional has been
well-established for various theoretical studies such as kinetic and
thermodynamic calculations related to Diels-Alder reactions of
fullerenes and metallofullerenes[49 ].This functional is a hybrid meta-GGA
functional which was developed by Zhao and Truhlar. It has been found
that Quasi-Newton methods are inefficient in finding the
transition-state structures (first-order saddle points) between the
equilibrium geometries. In this regard, Gaussian incorporates
Synchronous Transit-guided Quasi-Newton (STQN) method to search for a
maximum along the parabola connecting the reactant and product[50 ]. A parallel intrinsic reaction
coordinate (IRC) calculation [51 ] has
also been performed to confirm whether the transition states connect the
right minima or not. Normal-mode analysis has been carried out at the
same level of theory to confirm whether the optimized structures are
local minima (no imaginary frequency) or transition state geometries
(one imaginary frequency).The relative energies of the intermediate
adduct (ΔEA) and transition state (ΔETS)
concerning the separated reactants are defined as:
ΔEA= E(intermediate
adduct)-E(fullerene/metallofullerene)-E(1,3-butadiene);
ΔETS= E(transition
state)-E(fullerene/metallofullerene)-E(1,3-butadiene).
The activation barrier (ΔEa) is defined as:
ΔEa= ΔETS-ΔEA.
All energies reported in the article are zero-point-corrected electronic
energy obtained at 0 K temperature and 1 atm pressure.
Moreover, kinetics study has also been performed to determine the rate
of all Multi-Diels-Alder reactions by employing Transition State Theory
(TST) [52, 53 ]. The entire kinetic study
has been performed with The Rate program[54 ].In this program, the molecular
rotations are treated classically and the vibrations are treated quantum
mechanically within the harmonic approximation. The rate constant (k)
values have been determined for a temperature range of 100 K - 1000 K
with 100 K temperature interval, keeping the pressure fixed at 1 atm.